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The biological master clock, suprachiasmatic nucleus (of rat and mouse), is composed of ~10,000 clock cells which are heterogeneous with respect to their circadian periods. Despite this inhomogeneity, an intact SCN maintains a very good degree of circadian phase (time) coherence which is vital for sustaining various circadian rhythmic activities, and it is supposedly achieved by not just one but a few different cell-to-cell coupling mechanisms, among which action potential (AP)-mediated connectivity is known to be essential. But, due to technical difficulties and limitations in experiments, so far very little information is available about the morphology of the connectivity at a cellular scale. Building upon this limited amount of information, here we exhaustively and systematically explore a large pool (~25,000) of various network morphologies to come up with some plausible network features of SCN networks. All candidates under consideration reflect an experimentally obtained 'indegree distribution' as well as a 'physical range distribution of afferent clock cells.' Then, importantly, with a set of multitude criteria based on the properties of SCN circadian phase waves in extrinsically perturbed as well as in their natural states, we select out appropriate model networks: Some important measures are, 1) level of phase dispersal and direction of wave propagation, 2) phase-resetting ability of the model networks subject to external circadian forcing, and 3) decay rate of perturbation induced "phase-singularities." The successful, realistic networks have several common features: 1) "indegree" and "outdegree" should have a positive correlation; 2) the cells in the SCN ventrolateral region (core) have a much larger total degree than that of the dorsal medial region (shell); 3) The number of intra-core edges is about 7.5 times that of intra-shell edges; and 4) the distance probability density function for the afferent connections fits well to a beta function. We believe that these newly identified network features would be a useful guide for future explorations on the very much unknown AP-mediated clock cell connectome within the SCN. Author summary: The suprachiasmatic nucleus (SCN) is a tiny nucleus located within a deep brain area, serving the role of the biological master clock for mammals. It is composed of approximately 10,000 clock cells and orchestrates all daily rhythms such as the sleep-wake cycle and heart-beat rate modulation. The SCN is a vitally important part of the brain. Any significant disruptions in the spatiotemporal circadian dynamics inside this small nucleus may potentially lead to circadian arrhythmia akin to cardiac arrhythmia. One of the key elements governing the spatiotemporal circadian dynamics is the SCN clock cell-to-cell network morphology, which is currently largely unknown and very difficult to decipher even with all up-to-date technologies in neuroscience. Therefore, the purpose of this paper is to come up with a mathematical model SCN that has a clock cell network morphology good enough that the model SCN's spatiotemporal phase dynamics during perturbed as well as unperturbed natural states best matches those measured in experiments. We find many interesting features, some of which are 1) the outdegree (number of efferent connections) of each clock cell should have a positive correlation to its indegree (number of afferent connections), 2) the total degree of the cells in the SCN 'core' region is in general much larger than that of the 'shell' region, 3) the number of intra-core edges is about 7.5 times that of intra-shell edges; and 4) the number of inter-subdivisional edges should be much less than that of intra-core edges. These features identified via model simulations should be a useful guide for future experimental explorations on the clock cell connectome within the SCN. [ABSTRACT FROM AUTHOR]

The enzyme nitrogenase reduces dinitrogen to ammonia utilizing electrons, protons, and energy obtained from the hydrolysis of ATP. Mo-dependent nitrogenase is a symmetric dimer, with each half comprising an ATP-dependent reductase, termed the Fe Protein, and a catalytic protein, known as the MoFe protein, which hosts the electron transfer P-cluster and the active-site metal cofactor (FeMo-co). A series of synchronized events for the electron transfer have been characterized experimentally, in which electron delivery is coupled to nucleotide hydrolysis and regulated by an intricate allosteric network. We report a graph theory analysis of the mechanical coupling in the nitrogenase complex as a key step to understanding the dynamics of allosteric regulation of nitrogen reduction. This analysis shows that regions near the active sites undergo large-scale, large-amplitude correlated motions that enable communications within each half and between the two halves of the complex. Computational predictions of mechanically regions were validated against an analysis of the solution phase dynamics of the nitrogenase complex via hydrogen-deuterium exchange. These regions include the P-loops and the switch regions in the Fe proteins, the loop containing the residue β-188Ser adjacent to the P-cluster in the MoFe protein, and the residues near the protein-protein interface. In particular, it is found that: (i) within each Fe protein, the switch regions I and II are coupled to the [4Fe-4S] cluster; (ii) within each half of the complex, the switch regions I and II are coupled to the loop containing β-188Ser; (iii) between the two halves of the complex, the regions near the nucleotide binding pockets of the two Fe proteins (in particular the P-loops, located over 130 Å apart) are also mechanically coupled. Notably, we found that residues next to the P-cluster (in particular the loop containing β-188Ser) are important for communication between the two halves. Author summary: Enzymatic function is often the result of a sequence of events, which include precisely synchronized electron, proton and substrate delivery, that goes beyond the mere chemistry at the active site. To achieve this level of sophistication, enzymes must exploit a network of long-range communication through which chemical events, such as the binding of an effector to an allosteric site, hydrolysis of ATP, or electrochemical activity at a given location, affect on the function of a remote site. The nitrogenase complex vividly exemplifies the hierarchical complexity of enzymes. Nitrogenase catalyzes the reduction of atmospheric dinitrogen to ammonia, whose activity is regulated by long-range mechanical coupling between distant parts of the complex. After decades since the first structure of the nitrogenase complex was solved, this coupling network is still unclear. We used a computationally inexpensive, yet accurate approach, which is based on graph theory, to elucidate how distant regions of the protein complex communicate with each other. In particular, our study provides valuable insights on how the two halves of nitrogenase communicate and what the most important regions for this communication are, laying out a strategy for future mechanistic studies. [ABSTRACT FROM AUTHOR]

In eukaryotes, DNA achieves a highly compact structure primarily due to its winding around the histone cores. The nature wrapping of DNA around histone core form a 1.7 left-handed superhelical turns, contributing to negative supercoiling in chromatin. During transcription, negative supercoils generated behind the polymerase during transcription may play a role in triggering nucleosome reassembly. To elucidate how supercoils influence the dynamics of wrapping of DNA around the histone cores, we developed a novel model to simulate the intricate interplay between DNA and histone. Our simulations reveal that both positively and negatively supercoiled DNAs are capable of wrapping around histone cores to adopt the nucleosome conformation. Notably, our findings confirm a strong preference for negative supercoiled DNA during nucleosome wrapping, and reveal that the both of the negative writhe and twist are beneficial to the formation of the DNA wrapping around histone. Additionally, the simulations of the multiple nucleosomes on the same DNA template indicate that the nucleosome tends to assemble in proximity to the original nucleosome. This advancement in understanding the spontaneous formation of nucleosomes may offer insights into the complex dynamics of chromatin assembly and the fundamental mechanisms governing the structure and function of chromatin. Author summary: The compacted organization of DNA within chromatin is primarily attributed to its intricate winding around histone cores. This winding process involves 1.7 left-handed superhelical turns around the histone core, contributing to the negative supercoiling within chromatin fibers. To gain deeper insights into how DNA supercoiling impacts the dynamics of DNA wrapping around histone cores, we first devised a novel computational model that simulates the intricate interplay between DNA and histone cores. The simulations reveal that both of the positively and negatively supercoiled DNA can spontaneously adopt the nucleosome conformation upon wrapping around the histone core, and demonstrated a strong preference for negative supercoiling during nucleosome wrapping. Additionally, the simulations of multiple nucleosomes assembling show that the nucleosome tends to assemble near original nucleosome. Finally, we examined that both the negative writhe and twist components are advantageous for the formation of the nucleosome. The studies shed light on the intricate dynamics underlying chromatin assembly and its functional implications. [ABSTRACT FROM AUTHOR]

The discrepancy between structural and functional connectivity in neural systems forms the challenge in understanding general brain functioning. To pinpoint a mapping between structure and function, we investigated the effects of (in)homogeneity in coupling structure and delays on synchronization behavior in networks of oscillatory neural masses by deriving the phase dynamics of these generic networks. For homogeneous delays, the structural coupling matrix is largely preserved in the coupling between phases, resulting in clustered stationary phase distributions. Accordingly, we found only a small number of synchronized groups in the network. Distributed delays, by contrast, introduce inhomogeneity in the phase coupling so that clustered stationary phase distributions no longer exist. The effect of distributed delays mimicked that of structural inhomogeneity. Hence, we argue that phase (de-)synchronization patterns caused by inhomogeneous coupling cannot be distinguished from those caused by distributed delays, at least not by the naked eye. The here-derived analytical expression for the effective coupling between phases as a function of structural coupling constitutes a direct relationship between structural and functional connectivity. Structural connectivity constrains synchronizability that may be modified by the delay distribution. This explains why structural and functional connectivity bear much resemblance albeit not a one-to-one correspondence. We illustrate this in the context of resting-state activity, using the anatomical connectivity structure reported by Hagmann and others. [ABSTRACT FROM AUTHOR]

A tight regulation of morphogen production is key for morphogen gradient formation and thereby for reproducible and organised organ development. Although many genetic interactions involved in the establishment of morphogen production domains are known, the biophysical mechanisms of morphogen source formation are poorly understood. Here we addressed this by focusing on the morphogen Sonic hedgehog (Shh) in the vertebrate neural tube. Shh is produced by the adjacently located notochord and by the floor plate of the neural tube. Using a data-constrained computational screen, we identified different possible mechanisms by which floor plate formation can occur, only one of which is consistent with experimental data. In this mechanism, the floor plate is established rapidly in response to Shh from the notochord and the dynamics of regulatory interactions within the neural tube. In this process, uniform activators and Shh-dependent repressors are key for establishing the floor plate size. Subsequently, the floor plate becomes insensitive to Shh and increases in size due to tissue growth, leading to scaling of the floor plate with neural tube size. In turn, this results in scaling of the Shh amplitude with tissue growth. Thus, this mechanism ensures a separation of time scales in floor plate formation, so that the floor plate domain becomes growth-dependent after an initial rapid establishment phase. Our study raises the possibility that the time scale separation between specification and growth might be a common strategy for scaling the morphogen gradient amplitude in growing organs. The model that we developed provides a new opportunity for quantitative studies of morphogen source formation in growing tissues. Author summary: As organs grow during development, molecules called morphogens instruct cells to adopt specific fates at the right place and time. Morphogens are produced in specialized source regions and spread through organs, forming gradients of concentration. How morphogen source regions form in growing organs and contribute to the establishment of morphogen gradients is poorly understood. In this study, we combine theory and experiments to investigate the formation of a key morphogen source in the developing mouse spinal cord called floor plate. Uncommitted spinal cord cells adopt floor plate identity in response to the morphogen Sonic hedgehog (Shh), which is produced by the adjacent notochord and by the floor plate cells themselves. Over time, the floor plate expands, producing more Shh. We found that in theory, the floor plate could expand by distinct mechanisms. In one scenario, Shh produced by the floor plate itself is used to convert more cells into floor plate. Alternatively, once a few cells are initially specified, the floor plate expands passively by tissue growth. Our experimental and theoretical analysis indicate that the latter scenario is the one that is relevant to the biological system. Similar temporal decoupling of specification and growth might occur in other growing organs. [ABSTRACT FROM AUTHOR]

A recent investigation of the effect of different antiretroviral drug classes on first phase dynamics of HIV RNA plasma virus levels has indicated that drugs acting at stages closer to viral production, such as the integrase inhibitor raltegravir, can produce a steeper first phase decay slope that may not be due to drug efficacy. Moreover it was found that for most drug classes the first phase transitions from a faster (phase IA) to a slightly slower decay region (phase IB) before the start of the usual second phase. Neither of these effects has been explained to date. We use a mathematical model that incorporates the different stages of the HIV viral life cycle in CD4+ T cells: viral entry, reverse transcription, integration, and viral production, to investigate the intracellular HIV mechanisms responsible for these complex plasma virus decay dynamics. We find differences in the phase IA slope across drug classes arise from a higher death rate of cells when they enter the productively infected stage post-integration, with a half-life of approximately 8 hours in this stage, whereas cells in earlier stages of the infection cycle have half-lives similar to uninfected cells. This implies any immune clearance is predominantly limited to the productive infection stage. We also show that the slowing of phase IA to phase IB at day 2 to 4 of monotherapy, depending on drug class, is a result of new rounds of infection. The level at which this slowing occurs is a better indicator of drug efficacy than the slope of the initial decay. [ABSTRACT FROM AUTHOR]

Propagating waves of activity can be evoked and can occur spontaneously in vivo and in vitro in cerebral cortex. These waves are thought to be instrumental in the propagation of information across cortical regions and as a means to modulate the sensitivity of neurons to subsequent stimuli. In normal tissue, the waves are sparse and tightly controlled by inhibition and other negative feedback processes. However, alterations of this balance between excitation and inhibition can lead to pathological behavior such as seizure-type dynamics (with low inhibition) or failure to propagate (with high inhibition). We develop a spiking one-dimensional network of neurons to explore the reliability and control of evoked waves and compare this to a cortical slice preparation where the excitability can be pharmacologically manipulated. We show that the waves enhance sensitivity of the cortical network to stimuli in specific spatial and temporal ways. To gain further insight into the mechanisms of propagation and transitions to pathological behavior, we derive a mean-field model for the synaptic activity. We analyze the mean-field model and a piece-wise constant approximation of it and study the stability of the propagating waves as spatial and temporal properties of the inhibition are altered. We show that that the transition to seizure-like activity is gradual but that the loss of propagation is abrupt and can occur via either the loss of existence of the wave or through a loss of stability leading to complex patterns of propagation. Author summary: Stimuli and other aspects of neuronal activity are carried across areas in the brain through the concerted activity of recurrently connected neurons. The activity is controlled through negative feedback from both inhibitory neurons and intrinsic currents in the excitatory neurons. Evoked activity often appears in the form of a traveling pulse of activity. In this paper we study the speed, magnitude, and other properties of these waves as various aspects of the negative feedback are altered through both computational modeling and manipulations of a slice of cortex. Inhibition enables information to be readily transmitted across distances without the neural activity blowing up into a seizure-like state. [ABSTRACT FROM AUTHOR]

Environmental changes play a critical role in determining the evolution of social dilemmas in many natural or social systems. Generally, the environmental changes include two prominent aspects: the global time-dependent fluctuations and the local strategy-dependent feedbacks. However, the impacts of these two types of environmental changes have only been studied separately, a complete picture of the environmental effects exerted by the combination of these two aspects remains unclear. Here we develop a theoretical framework that integrates group strategic behaviors with their general dynamic environments, where the global environmental fluctuations are associated with a nonlinear factor in public goods game and the local environmental feedbacks are described by the 'eco-evolutionary game'. We show how the coupled dynamics of local game-environment evolution differ in static and dynamic global environments. In particular, we find the emergence of cyclic evolution of group cooperation and local environment, which forms an interior irregular loop in the phase plane, depending on the relative changing speed of both global and local environments compared to the strategic change. Further, we observe that this cyclic evolution disappears and transforms into an interior stable equilibrium when the global environment is frequency-dependent. Our results provide important insights into how diverse evolutionary outcomes could emerge from the nonlinear interactions between strategies and the changing environments. Author summary: The intricate interplay between strategic behavior and environment is ubiquitous in complex systems of different scales. Previous works mainly focus on one aspect of the environmental changes: either global environment fluctuations that unidirectionally decide the welfare of the evolutionary dynamics, or local environment feedbacks that coevolve with the strategic behavior. Here we develop a theoretical framework that integrates them both in order to obtain a more complete picture of how group cooperation evolves in a general dynamic environment. We show that global environmental fluctuations can fundamentally alter the dynamical predictions of local game-environment evolution. The most interesting finding is the emergence of cyclic evolution of group cooperation and local environment, which forms an interior irregular loop in the phase plane, depending on the relative changing speed of both global and local environments compared to the strategic change. Such irregular loop, however, is substituted by an interior stable fixed point when considering a more complicated situation where the global environment is also frequency-dependent. Our results show how rich dynamical outcomes arise from the interactions between strategic behaviors and their natural or social environments, which has important practical value for solving social dilemmas in an ever-changing world. [ABSTRACT FROM AUTHOR]

Reduced cortical inhibition by somatostatin-expressing (SST) interneurons has been strongly associated with treatment-resistant depression. However, due to technical limitations it is impossible to establish experimentally in humans whether the effects of reduced SST interneuron inhibition on microcircuit activity have signatures detectable in clinically-relevant brain signals such as electroencephalography (EEG). To overcome these limitations, we simulated resting-state activity and EEG using detailed models of human cortical microcircuits with normal (healthy) or reduced SST interneuron inhibition (depression), and found that depression microcircuits exhibited increased theta, alpha and low beta power (4–16 Hz). The changes in depression involved a combination of an aperiodic broadband and periodic theta components. We then demonstrated the specificity of the EEG signatures of reduced SST interneuron inhibition by showing they were distinct from those corresponding to reduced parvalbumin-expressing (PV) interneuron inhibition. Our study thus links SST interneuron inhibition level to distinct features in EEG simulated from detailed human microcircuits, which can serve to better identify mechanistic subtypes of depression using EEG, and non-invasively monitor modulation of cortical inhibition. Author summary: Reduced somatostatin-expressing interneuron (SST) inhibition has been implicated in depression. However, it is impossible to establish experimentally in humans how these inhibitory changes are reflected in clinically relevant brain signals (electroencephalography, EEG). We performed detailed simulations of human neuronal network activity and EEG signals in health and depression. We found that reduced SST inhibition led to significant changes in EEG, which accounts for changes seen in depression. Our study thus provides biomarkers that link inhibition level of a key interneuron type to measurable signatures in EEG. These biomarkers can be used to identify subtypes of depression and non-invasively monitor cortical inhibition modulation. [ABSTRACT FROM AUTHOR]

Despite the considerable progress of in vivo neural recording techniques, inferring the biophysical mechanisms underlying large scale coordination of brain activity from neural data remains challenging. One obstacle is the difficulty to link high dimensional functional connectivity measures to mechanistic models of network activity. We address this issue by investigating spike-field coupling (SFC) measurements, which quantify the synchronization between, on the one hand, the action potentials produced by neurons, and on the other hand mesoscopic "field" signals, reflecting subthreshold activities at possibly multiple recording sites. As the number of recording sites gets large, the amount of pairwise SFC measurements becomes overwhelmingly challenging to interpret. We develop Generalized Phase Locking Analysis (GPLA) as an interpretable dimensionality reduction of this multivariate SFC. GPLA describes the dominant coupling between field activity and neural ensembles across space and frequencies. We show that GPLA features are biophysically interpretable when used in conjunction with appropriate network models, such that we can identify the influence of underlying circuit properties on these features. We demonstrate the statistical benefits and interpretability of this approach in various computational models and Utah array recordings. The results suggest that GPLA, used jointly with biophysical modeling, can help uncover the contribution of recurrent microcircuits to the spatio-temporal dynamics observed in multi-channel experimental recordings. Author summary: Modern neural recording techniques give access to increasingly highly multivariate spike data, together with spatio-temporal activities of local field potentials reflecting integrative processes. We introduce GPLA as a generalized coupling measure between these point-process and continuous-time activities to help neuroscientists uncover the distributed organization of neural networks. We develop statistical analysis and modeling methodologies for this measure and demonstrate its interpretability in simulated and experimental multi-electrode recordings. [ABSTRACT FROM AUTHOR]

Neural mass models are used to simulate cortical dynamics and to explain the electrical and magnetic fields measured using electro- and magnetoencephalography. Simulations evince a complex phase-space structure for these kinds of models; including stationary points and limit cycles and the possibility for bifurcations and transitions among different modes of activity. This complexity allows neural mass models to describe the itinerant features of brain dynamics. However, expressive, nonlinear neural mass models are often difficult to fit to empirical data without additional simplifying assumptions: e.g., that the system can be modelled as linear perturbations around a fixed point. In this study we offer a mathematical analysis of neural mass models, specifically the canonical microcircuit model, providing analytical solutions describing slow changes in the type of cortical activity, i.e. dynamical itinerancy. We derive a perturbation analysis up to second order of the phase flow, together with adiabatic approximations. This allows us to describe amplitude modulations in a relatively simple mathematical format providing analytic proof-of-principle for the existence of semi-stable states of cortical dynamics at the scale of a cortical column. This work allows for model inversion of neural mass models, not only around fixed points, but over regions of phase space that encompass transitions among semi or multi-stable states of oscillatory activity. Crucially, these theoretical results speak to model inversion in the context of multiple semi-stable brain states, such as the transition between interictal, pre-ictal and ictal activity in epilepsy. Author summary: There is collecting evidence that the electrical activity of the brain is highly complex. Electro- and magnetoencephalography, being non-invasive methods, are often used to measure brain function in humans and have provided a large amount of data indicating complexity. Furthermore, a quantitative framework is required to understand the interactions between the different features of electrical activity of the brain. Neural mass models can provide a quantitative framework required to further understand brain activity and complexity, and in this paper we provide a mathematical form that can be used to understand some of the complex electrical dynamics of the brain. Crucially, these theoretical results improve our understanding of multiple semi-stable brain states, as seen in epilepsy. [ABSTRACT FROM AUTHOR]

Tumor necrosis factor alpha (TNFα) is a well-known modulator of apoptosis by maintaining a balance between proliferation and cell-death in normal cells. Cancer cells often evade apoptotic response following TNFα stimulation by altering signaling cross-talks. Thus, varying the extent of signaling cross-talk could enable optimal TNFα mediated apoptotic dynamics. Herein, we use an experimental data-driven mathematical modeling to quantitate the extent of synergistic signaling cross-talk between the intracellular entities phosphorylated JNK (pJNK) and phosphorylated AKT (pAKT) that orchestrate the phenotypic apoptosis level by modulating the activated Caspase3 dynamics. Our study reveals that this modulation is orchestrated by the distinct dynamic nature of the synergism at early and late phases. We show that this synergism in signal flow is governed by branches originating from either TNFα receptor and NFκB, which facilitates signaling through survival pathways. We demonstrate that the experimentally quantified apoptosis levels semi-quantitatively correlates with the model simulated Caspase3 transients. Interestingly, perturbing pJNK and pAKT transient dynamics fine-tunes this accumulated Caspase3 guided apoptotic response. Thus, our study offers useful insights for identifying potential targeted therapies for optimal apoptotic response. Author summary: TNFα mediated apoptosis, a form of cell-death, is the desired outcome for cancer therapeutics. This outcome is governed by complex regulation involving several signaling entities stimulated by TNFα. Relating the transient levels of these entities over early phase of the signaling response to the late-phase cell-death is a challenge. We developed a knowledge and data-driven mathematical model to unravel the dynamic synergistic correlation between the early transients governing the apoptotic response. Using flux balance and branch analysis, we demonstrated that the dynamic cross-talk between different key signaling entities regulates the apoptotic response. We performed inhibitory experiments predicted by model simulations and thereby established that cells tweak the extent of synergism during signal transduction to modulate the apoptotic response in a time-dependent manner. Thus, our approach provides useful insights for identifying signaling targets to arrive at novel combinatorial cancer therapies. [ABSTRACT FROM AUTHOR]

In Escherichia coli, translocation of RNA polymerase (RNAP) during transcription introduces supercoiling to DNA, which influences the initiation and elongation behaviors of RNAP. To quantify the role of supercoiling in transcription regulation, we developed a spatially resolved supercoiling model of transcription. The integrated model describes how RNAP activity feeds back with the local DNA supercoiling and how this mechanochemical feedback controls transcription, subject to topoisomerase activities and stochastic topological domain formation. This model establishes that transcription-induced supercoiling mediates the cooperation of co-transcribing RNAP molecules in highly expressed genes, and this cooperation is achieved under moderate supercoiling diffusion and high topoisomerase unbinding rates. It predicts that a topological domain could serve as a transcription regulator, generating substantial transcriptional noise. It also shows the relative orientation of two closely arranged genes plays an important role in regulating their transcription. The model provides a quantitative platform for investigating how genome organization impacts transcription. Author summary: DNA mechanics and transcription dynamics are intimately coupled. During transcription, the translocation of RNA polymerase overwinds the DNA ahead and underwinds the DNA behind, rendering the DNA supercoiled. The supercoiled DNA could, in return, influences the behavior of the RNA polymerase, and consequently the amount of mRNA product it makes. Furthermore, supercoils could propagate on the DNA over thousands of base pairs, impacting RNA polymerase molecules at faraway sites. These complicated interplays between supercoiling and RNA polymerase makes supercoiling an important transcription regulator. To quantitatively investigate the role of supercoiling in transcription, we build a spatially resolved model that links transcription with the generation, propagation, and dissipation of supercoiling. Our model reveals that supercoiling mediates transcription at multiple length scales. At a single-gene scale, we show that supercoiling gives rise to the collective motion of co-transcribing RNA polymerase molecules, supporting recent experimental observations. Additionally, large variations in mRNA production of a gene can arise from the constraints of supercoiling diffusion in a topological domain. At a multi-gene scale, we show that supercoiling dynamics allow two adjacent genes influence each other's transcription kinetics, thus serving as a transcription regulator. [ABSTRACT FROM AUTHOR]

Macroscopic oscillations in the brain have been observed to be involved in many cognitive tasks but their role is not completely understood. One of the suggested functions of the oscillations is to dynamically modulate communication between neural circuits. The Communication Through Coherence (CTC) theory proposes that oscillations reflect rhythmic changes in excitability of the neuronal populations. Thus, populations need to be properly phase-locked so that input volleys arrive at the peaks of excitability of the receiving population to communicate effectively. Here, we present a modeling study to explore synchronization between neuronal circuits connected with unidirectional projections. We consider an Excitatory-Inhibitory (E-I) network of quadratic integrate-and-fire neurons modeling a Pyramidal-Interneuronal Network Gamma (PING) rhythm. The network receives an external periodic input from either one or two sources, simulating the inputs from other oscillating neural groups. We use recently developed mean-field models which provide an exact description of the macroscopic activity of the spiking network. This low-dimensional mean field model allows us to use tools from bifurcation theory to identify the phase-locked states between the input and the target population as a function of the amplitude, frequency and coherence of the inputs. We identify the conditions for optimal phase-locking and effective communication. We find that inputs with high coherence can entrain the network for a wider range of frequencies. Besides, faster oscillatory inputs than the intrinsic network gamma cycle show more effective communication than inputs with similar frequency. Our analysis further shows that the entrainment of the network by inputs with higher frequency is more robust to distractors, thus giving them an advantage to entrain the network and communicate effectively. Finally, we show that pulsatile inputs can switch between attended inputs in selective attention. Author summary: Oscillations are ubiquitous in the brain and are involved in several cognitive tasks but their role is not completely understood. The Communication Through Coherence theory proposes that background oscillations in the brain regulate the information flow between neural populations. The oscillators that are properly phase-locked so that inputs arrive at the peaks of excitability of the receiving population communicate effectively. In this paper, we study the emerging phase-locking patterns of a network generating PING oscillations under external periodic forcing, simulating the oscillatory input from other neural groups. We identify the conditions for optimal phase-locking and effective communication. Namely, we find that inputs with higher frequency and coherence have an adavantage to entrain the network and we quantify how robust are to distractors. Furthermore, we show how selective attention can be implemented by means of phase locking and we show that pulsatile inputs can switch between attended inputs. [ABSTRACT FROM AUTHOR]

Synchronization of neural oscillations is thought to facilitate communication in the brain. Neurodegenerative pathologies such as Parkinson's disease (PD) can result in synaptic reorganization of the motor circuit, leading to altered neuronal dynamics and impaired neural communication. Treatments for PD aim to restore network function via pharmacological means such as dopamine replacement, or by suppressing pathological oscillations with deep brain stimulation. We tested the hypothesis that brain stimulation can operate beyond a simple "reversible lesion" effect to augment network communication. Specifically, we examined the modulation of beta band (14–30 Hz) activity, a known biomarker of motor deficits and potential control signal for stimulation in Parkinson's. To do this we setup a neural mass model of population activity within the cortico-basal ganglia-thalamic (CBGT) circuit with parameters that were constrained to yield spectral features comparable to those in experimental Parkinsonism. We modulated the connectivity of two major pathways known to be disrupted in PD and constructed statistical summaries of the spectra and functional connectivity of the resulting spontaneous activity. These were then used to assess the network-wide outcomes of closed-loop stimulation delivered to motor cortex and phase locked to subthalamic beta activity. Our results demonstrate that the spatial pattern of beta synchrony is dependent upon the strength of inputs to the STN. Precisely timed stimulation has the capacity to recover network states, with stimulation phase inducing activity with distinct spectral and spatial properties. These results provide a theoretical basis for the design of the next-generation brain stimulators that aim to restore neural communication in disease. Author summary: Diseases of the brain lead to a wide range of disabling symptoms for patients, by affecting their ability to move or think properly. These symptoms arise from disruption to both the organization of networks in the brain, but also the timing of neural activity that propagates around it. Treatments for disease with drugs can restore the organization of these networks to some extent, yet it is very difficult to deliver drugs with good spatial or temporal selectivity. Brain stimulation provides one way in which to improve the spatial specificity of treatment, yet understanding how to stimulate at the right time to achieve the best outcome for patients, remains an outstanding question. In this work we use simulations of an important circuit involved in Parkinson's disease that has parameters chosen to reflect recordings made in animal models of the disease. Using this computer model, we show how brain rhythms can act as signatures of underlying changes in networks. Further, we simulate intervention with temporally precise stimulation to show how future approaches to brain stimulation can act to restore or even augment neural networks following their degeneration in disease. [ABSTRACT FROM AUTHOR]

Neural oscillations are evident across cortex but their spatial structure is not well- explored. Are oscillations stationary or do they form "traveling waves", i.e., spatially organized patterns whose peaks and troughs move sequentially across cortex? Here, we show that oscillations in the prefrontal cortex (PFC) organized as traveling waves in the theta (4-8Hz), alpha (8-12Hz) and beta (12-30Hz) bands. Some traveling waves were planar but most rotated. The waves were modulated during performance of a working memory task. During baseline conditions, waves flowed bidirectionally along a specific axis of orientation. Waves in different frequency bands could travel in different directions. During task performance, there was an increase in waves in one direction over the other, especially in the beta band. Author summary: We found that oscillations in the prefrontal cortex form "traveling waves". Traveling waves are spatially extended patterns in which aligned peaks of activity move sequentially across the cortical surface. Some traveling waves were planar but most rotated. The prefrontal cortex is important for working memory. The traveling waves changed when monkeys performed a working memory task. There was an increase in waves in one direction over the other, especially in the beta band. Traveling waves can serve specific functions. For example, they help maintain network status and help control timing relationships between spikes. Given their functional advantages, a greater understanding of traveling waves should lead to a greater understanding of cortical function. [ABSTRACT FROM AUTHOR]

The generation of neural action potentials (spikes) is random but nevertheless may result in a rich statistical structure of the spike sequence. In particular, contrary to the popular renewal assumption of theoreticians, the intervals between adjacent spikes are often correlated. Experimentally, different patterns of interspike-interval correlations have been observed and computational studies have identified spike-frequency adaptation and correlated noise as the two main mechanisms that can lead to such correlations. Analytical studies have focused on the single cases of either correlated (colored) noise or adaptation currents in combination with uncorrelated (white) noise. For low-pass filtered noise or adaptation, the serial correlation coefficient can be approximated as a single geometric sequence of the lag between the intervals, providing an explanation for some of the experimentally observed patterns. Here we address the problem of interval correlations for a widely used class of models, multidimensional integrate-and-fire neurons subject to a combination of colored and white noise sources and a spike-triggered adaptation current. Assuming weak noise, we derive a simple formula for the serial correlation coefficient, a sum of two geometric sequences, which accounts for a large class of correlation patterns. The theory is confirmed by means of numerical simulations in a number of special cases including the leaky, quadratic, and generalized integrate-and-fire models with colored noise and spike-frequency adaptation. Furthermore we study the case in which the adaptation current and the colored noise share the same time scale, corresponding to a slow stochastic population of adaptation channels; we demonstrate that our theory can account for a nonmonotonic dependence of the correlation coefficient on the channel's time scale. Another application of the theory is a neuron driven by network-noise-like fluctuations (green noise). We also discuss the range of validity of our weak-noise theory and show that by changing the relative strength of white and colored noise sources, we can change the sign of the correlation coefficient. Finally, we apply our theory to a conductance-based model which demonstrates its broad applicability. Author summary: The elementary processing units in the central nervous system are neurons that transmit information by short electrical pulses, so called action potentials or spikes. The generation of the action potential is a random process that can be shaped by correlated fluctuations (colored noise) and by adaptation. A consequence of these two ubiquitous features is that the successive time intervals between spikes, the interspike intervals, are not independent but correlated. As these correlations can significantly improve information transmission and weak-signal detection, it is an important task to develop analytical approaches to these statistics for well-established computational models. Here we present a theory of interval correlations for a widely used class of integrate-and-fire models endowed with an adaptation mechanism and subject to correlated fluctuations. We demonstrate which patterns of interval correlations can be expected from the interplay of colored noise, adaptation and intrinsic nonlinear dynamics. [ABSTRACT FROM AUTHOR]

Stroke is a debilitating condition affecting millions of people worldwide. The development of improved rehabilitation therapies rests on finding biomarkers suitable for tracking functional damage and recovery. To achieve this goal, we perform a spatiotemporal analysis of cortical activity obtained by wide-field calcium images in mice before and after stroke. We compare spontaneous recovery with three different post-stroke rehabilitation paradigms, motor training alone, pharmacological contralesional inactivation and both combined. We identify three novel indicators that are able to track how movement-evoked global activation patterns are impaired by stroke and evolve during rehabilitation: the duration, the smoothness, and the angle of individual propagation events. Results show that, compared to pre-stroke conditions, propagation of cortical activity in the subacute phase right after stroke is slowed down and more irregular. When comparing rehabilitation paradigms, we find that mice treated with both motor training and pharmacological intervention, the only group associated with generalized recovery, manifest new propagation patterns, that are even faster and smoother than before the stroke. In conclusion, our new spatiotemporal propagation indicators could represent promising biomarkers that are able to uncover neural correlates not only of motor deficits caused by stroke but also of functional recovery during rehabilitation. In turn, these insights could pave the way towards more targeted post-stroke therapies. Author summary: Millions of people worldwide suffer from long-lasting motor deficits caused by stroke. Very recently, the two basic therapeutic approaches, motor training and pharmacological intervention, have been combined in order to achieve a more efficient functional recovery. In this study, we analyze the neurophysiological activity in the brain of mice observed with in vivo calcium imaging before and after the induction of a stroke. We use a newly developed universal approach based on the temporal sequence of local activation in different brain regions to quantify three properties of global propagation patterns: duration, smoothness and angle. These innovative spatiotemporal propagation indicators allow us to track damage and functional recovery following stroke and to quantify the relative success of motor training, pharmacological inactivation, and a combination of both, compared to spontaneous recovery. We show that all three treatments reverse the alterations observed during the subacute phase right after stroke. We also find that combining motor training and pharmacological intervention does not restore pre-stroke features but rather leads to the emergence of new propagation patterns that, surprisingly, are even faster and smoother than the pre-stroke patterns. [ABSTRACT FROM AUTHOR]

Metastability in the brain is thought to be a mechanism involved in dynamic organization of cognitive and behavioral functions across multiple spatiotemporal scales. However, it is not clear how such organization is realized in underlying neural oscillations in a high-dimensional state space. It was shown that macroscopic oscillations often form phase-phase coupling (PPC) and phase-amplitude coupling (PAC) which result in synchronization and amplitude modulation, respectively, even without external stimuli. These oscillations can also make spontaneous transitions across synchronous states at rest. Using resting-state electroencephalographic signals and the autism-spectrum quotient scores acquired from healthy humans, we show experimental evidence that the PAC combined with PPC allows amplitude modulation to be transient, and that the metastable dynamics with this transient modulation is associated with autistic-like traits. In individuals with a longer attention span, such dynamics tended to show fewer transitions between states by forming delta-alpha PAC. We identified these states as two-dimensional metastable states that could share consistent patterns across individuals. Our findings suggest that the human brain dynamically organizes inter-individual differences in a hierarchy of macroscopic oscillations with multiple timescales by utilizing metastability. Author summary: The human brain organizes cognitive and behavioral functions dynamically. For decades, the dynamic organization of underlying neural oscillations has been a fundamental topic in neuroscience research. Even without external stimuli, macroscopic oscillations often form phase-phase coupling and phase-amplitude coupling (PAC) that result in synchronization and amplitude modulation, respectively, and can make spontaneous transitions across synchronous states at rest. Using resting-state electroencephalography signals acquired from healthy humans, we show evidence that these two neural couplings enable amplitude modulation to be transient, and that this transient modulation can be viewed as the transition among oscillatory states with different PAC strengths. We also demonstrate that such transition dynamics are associated with the ability to maintain attention to detail and to switch attention, as measured by autism-spectrum quotient scores. These individual dynamics were visualized as a trajectory among states with attracting tendencies, and involved consistent brain states across individuals. Our findings have significant implications for unraveling variability in the individual brains showing typical and atypical development. [ABSTRACT FROM AUTHOR]

Brain networks exhibit very variable and dynamical functional connectivity and flexible configurations of information exchange despite their overall fixed structure. Brain oscillations are hypothesized to underlie time-dependent functional connectivity by periodically changing the excitability of neural populations. In this paper, we investigate the role of the connection delay and the detuning between the natural frequencies of neural populations in the transmission of signals. Based on numerical simulations and analytical arguments, we show that the amount of information transfer between two oscillating neural populations could be determined by their connection delay and the mismatch in their oscillation frequencies. Our results highlight the role of the collective phase response curve of the oscillating neural populations for the efficacy of signal transmission and the quality of the information transfer in brain networks. Author summary: Collective dynamics in brain networks are characterized by a coordinated activity of their constituent neurons that lead to brain oscillations. Many evidences highlight the role that brain oscillations play in signal transmission, the control of the effective communication between brain areas, and the integration of information processed by different specialized regions. Oscillations periodically modulate the excitability of neurons and determine the response of those areas receiving the signals. Based on the communication through coherence (CTC) theory, the adjustment of the phase difference between local oscillations of connected areas can specify the timing of exchanged signals and therefore, the efficacy of the communication channels. In this respect, an important factor is the delay in the transmission of signals from one region to another that affects the phase difference and timing, and consequently the impact of the signals. Despite this delay plays an essential role in CTC theory, its role has been mostly overlooked in previous studies. In this manuscript, we concentrate on the role that the connection delay and the oscillation frequency of the populations play in the signal transmission, and consequently in the effective connectivity, between two brain areas. Through extensive numerical simulations, as well as analytical results with reduced models, we show that these parameters have two essential impacts on the effective connectivity of neural networks: First, that the populations advancing in phase to others do not necessarily play the role of the information source; and second, that the amount and direction of information transfer dependents on the oscillation frequency of the populations. [ABSTRACT FROM AUTHOR]

The mechanisms underlying the emergence of seizures are one of the most important unresolved issues in epilepsy research. In this paper, we study how perturbations, exogenous or endogenous, may promote or delay seizure emergence. To this aim, due to the increasingly adopted view of epileptic dynamics in terms of slow-fast systems, we perform a theoretical analysis of the phase response of a generic relaxation oscillator. As relaxation oscillators are effectively bistable systems at the fast time scale, it is intuitive that perturbations of the non-seizing state with a suitable direction and amplitude may cause an immediate transition to seizure. By contrast, and perhaps less intuitively, smaller amplitude perturbations have been found to delay the spontaneous seizure initiation. By studying the isochrons of relaxation oscillators, we show that this is a generic phenomenon, with the size of such delay depending on the slow flow component. Therefore, depending on perturbation amplitudes, frequency and timing, a train of perturbations causes an occurrence increase, decrease or complete suppression of seizures. This dependence lends itself to analysis and mechanistic understanding through methods outlined in this paper. We illustrate this methodology by computing the isochrons, phase response curves and the response to perturbations in several epileptic models possessing different slow vector fields. While our theoretical results are applicable to any planar relaxation oscillator, in the motivating context of epilepsy they elucidate mechanisms of triggering and abating seizures, thus suggesting stimulation strategies with effects ranging from mere delaying to full suppression of seizures. Author summary: Despite its simplicity, the modelling of epileptic dynamics as a slow-fast transition between low and high activity states mediated by some slow feedback variable is a relatively novel albeit fruitful approach. This study is the first, to our knowledge, characterizing the response of such slow-fast models of epileptic brain to perturbations by computing its isochrons. Besides its numerical computation, we theoretically determine which factors shape the geometry of isochrons for planar slow-fast oscillators. As a consequence, we introduce a theoretical approach providing a clear understanding of the response of perturbations of slow-fast oscillators. Within the epilepsy context, this elucidates the origin of the contradictory role of interictal epileptiform discharges in the transition to seizure, manifested by both pro-convulsive and anti-convulsive effect depending on the amplitude, frequency and timing. More generally, this paper provides theoretical framework highlighting the role of the slow flow component on the response to perturbations in relaxation oscillators, pointing to the general phenomena in such slow-fast oscillators ubiquitous in biological systems. [ABSTRACT FROM AUTHOR]

The molecular circadian clock is driven by interlocked transcriptional-translational feedback loops, producing oscillations in the expressions of genes and proteins to coordinate the timing of biological processes throughout the body. Modeling this system gives insight into the underlying processes driving oscillations in an activator-repressor architecture and allows us to make predictions about how to manipulate these oscillations. The knockdown or upregulation of different cellular components using small molecules can disrupt these rhythms, causing a phase shift, and we aim to determine the dosing of such molecules with a model-based control strategy. Mathematical models allow us to predict the phase response of the circadian clock to these interventions and time them appropriately but only if the model has enough physiological detail to describe these responses while maintaining enough simplicity for online optimization. We build a control-relevant, physiologically-based model of the two main feedback loops of the mammalian molecular clock, which provides sufficient detail to consider multi-input control. Our model captures experimentally observed peak to trough ratios, relative abundances, and phase differences in the model species, and we independently validate this model by showing that the in silico model reproduces much of the behavior that is observed in vitro under genetic knockout conditions. Because our model produces valid phase responses, it can be used in a model predictive control algorithm to determine inputs to shift phase. Our model allows us to consider multi-input control through small molecules that act on both feedback loops, and we find that changes to the parameters of the negative feedback loop are much stronger inputs for shifting phase. The strongest inputs predicted by this model provide targets for new experimental small molecules and suggest that the function of the positive feedback loop is to stabilize the oscillations while linking the circadian system to other clock-controlled processes. Author summary: The circadian clock helps to regulate many biological functions, including the sleep-wake cycle, metabolism, the cardiovascular system, and the immune response, so we can promote better health by aligning the internal body clock to the phase of the external environment. At the cellular level, the circadian clock is driven by the interactions of a core set of genes and proteins, presenting inputs to manipulate the clock. Mathematical models allow us to predict which inputs can best be used to shift the internal clock to align with the environment. In this paper, we develop a model, consisting of a system of differential equations, to describe the molecular level components which drive circadian rhythms and test the model to show it captures experimental observations. We then use this model to determine what parametric changes have the strongest resetting effect on the clock, suggesting which mechanisms the development of new experimental small molecules should target to most efficiently shift circadian phase. We demonstrate the efficacy of this approach in a model predictive control simulation. Although we build a model specific to the circadian clock, the techniques we describe for modeling and control of the circadian oscillator can be applied to many oscillating systems. [ABSTRACT FROM AUTHOR]

While highly active antiretroviral therapy (HAART) is successful in controlling the replication of Human Immunodeficiency Virus (HIV-1) in many patients, currently there is no cure for HIV-1, presumably due to the presence of reservoirs of the virus. One of the least studied viral reservoirs is the brain, which the virus enters by crossing the blood-brain barrier (BBB) via macrophages, which are considered as conduits between the blood and the brain. The presence of HIV-1 in the brain often leads to HIV associated neurocognitive disorders (HAND), such as encephalitis and early-onset dementia. In this study we develop a novel mathematical model that describes HIV-1 infection in the brain and in the plasma coupled via the BBB. The model predictions are consistent with data from macaques infected with a mixture of simian immunodeficiency virus (SIV) and simian-human immunodeficiency virus (SHIV). Using our model, we estimate the rate of virus transport across the BBB as well as viral replication inside the brain, and we compute the basic reproduction number. We also carry out thorough sensitivity analysis to define the robustness of the model predictions on virus dynamics inside the brain. Our model provides useful insight into virus replication within the brain and suggests that the brain can be an important reservoir causing long-term viral persistence. Author summary: Around the world HIV/AIDS remains among the most disastrous disease epidemics that humanity is facing. Currently several treatment regimens and drugs exist that can prolong the life of HIV infected individuals, but none can cure the disease. As the virus remains within infected individuals for life, including in their brain, a long lifespan leads to HIV associated neurocognitive disorders (HAND) such as encephalitis or early-onset dementia. Here we develop a mathematical model to study the viral dynamics in the brain. Our model, which can accurately describe experimental data from macaques, predicts a significantly high rate of HIV transport in and out of the brain through the blood-brain barrier (BBB). The possibility of ongoing HIV replication inside the brain predicted by our model indicates that the brain can be an important viral reservoir causing an obstacle to an HIV cure. This suggests that eradication of the virus inside the brain should also be considered while designing strategies for HIV cure. [ABSTRACT FROM AUTHOR]

Thoughtful use of simplifying assumptions is crucial to make systems biology models tractable while still representative of the underlying biology. A useful simplification can elucidate the core dynamics of a system. A poorly chosen assumption can, however, either render a model too complicated for making conclusions or it can prevent an otherwise accurate model from describing experimentally observed dynamics. Here, we perform a computational investigation of sequential multi-step pathway models that contain fewer pathway steps than the system they are designed to emulate. We demonstrate when such models will fail to reproduce data and how detrimental truncation of a pathway leads to detectable signatures in model dynamics and its optimised parameters. An alternative assumption is suggested for simplifying such pathways. Rather than assuming a truncated number of pathway steps, we propose to use the assumption that the rates of information propagation along the pathway is homogeneous and, instead, letting the length of the pathway be a free parameter. We first focus on linear pathways that are sequential and have first-order kinetics, and we show how this assumption results in a three-parameter model that consistently outperforms its truncated rival and a delay differential equation alternative in recapitulating observed dynamics. We then show how the proposed assumption allows for similarly terse and effective models of non-linear pathways. Our results provide a foundation for well-informed decision making during model simplifications. Author summary: Mathematical modelling can be a highly effective way of condensing our understanding of biological processes and highlight the most important aspects of them. Effective models are based on simplifying assumptions that reduce complexity while still retaining the core dynamics of the original problem. Finding such assumptions is, however, not trivial. In this paper, we explore ways in which one can simplify long chains of simple reactions wherein each step is only dependent on its predecessor. After generating synthetic data from models that describe such chains in explicit detail we compare how well different simplifications retain the original dynamics. We show that the most common such simplification, which is to ignore parts of the chain, often renders models unable to account for time delays. However, we also show that when such a simplification has had a detrimental effect it leaves a detectable signature in its optimised parameter values. We also propose an alternative assumption which leads to a highly effective model with only three parameters. By comparing the effects of these simplifying assumptions in thousands of different cases and for different conditions we are able to clearly show when and why one is preferred over the other. [ABSTRACT FROM AUTHOR]

Circadian rhythms are generated by interlocked transcriptional-translational negative feedback loops (TTFLs), the molecular process implemented within a cell. The contributions, weighting and balancing between the multiple feedback loops remain debated. Dissociated, free-running dynamics in the expression of distinct clock genes has been described in recent experimental studies that applied various perturbations such as slice preparations, light pulses, jet-lag, and culture medium exchange. In this paper, we provide evidence that this “presumably transient” dissociation of circadian gene expression oscillations may occur at the single-cell level. Conceptual and detailed mechanistic mathematical modeling suggests that such dissociation is due to a weak interaction between multiple feedback loops present within a single cell. The dissociable loops provide insights into underlying mechanisms and general design principles of the molecular circadian clock. [ABSTRACT FROM AUTHOR]

Most biological systems are difficult to analyse due to a multitude of interacting components and the concomitant lack of information about the essential dynamics. Finding appropriate models that provide a systematic description of such biological systems and that help to identify their relevant factors and processes can be challenging given the sheer number of possibilities. Model selection algorithms that evaluate the performance of a multitude of different models against experimental data provide a useful tool to identify appropriate model structures. However, many algorithms addressing the analysis of complex dynamical systems, as they are often used in biology, compare a preselected number of models or rely on exhaustive searches of the total model space which might be unfeasible dependent on the number of possibilities. Therefore, we developed an algorithm that is able to perform model selection on complex systems and searches large model spaces in a dynamical way. Our algorithm includes local and newly developed non-local search methods that can prevent the algorithm from ending up in local minima of the model space by accounting for structurally similar processes. We tested and validated the algorithm based on simulated data and showed its flexibility for handling different model structures. We also used the algorithm to analyse experimental data on the cell proliferation dynamics of CD4+ and CD8+ T cells that were cultured under different conditions. Our analyses indicated dynamical changes within the proliferation potential of cells that was reduced within tissue-like 3D ex vivo cultures compared to suspension. Due to the flexibility in handling various model structures, the algorithm is applicable to a large variety of different biological problems and represents a useful tool for the data-oriented evaluation of complex model spaces. [ABSTRACT FROM AUTHOR]

Neuronal oscillations are ubiquitous in the human brain and are implicated in virtually all brain functions. Although they can be described by a prominent peak in the power spectrum, their waveform is not necessarily sinusoidal and shows rather complex morphology. Both frequency and temporal descriptions of such non-sinusoidal neuronal oscillations can be utilized. However, in non-invasive EEG/MEG recordings the waveform of oscillations often takes a sinusoidal shape which in turn leads to a rather oversimplified view on oscillatory processes. In this study, we show in simulations how spatial synchronization can mask non-sinusoidal features of the underlying rhythmic neuronal processes. Consequently, the degree of non-sinusoidality can serve as a measure of spatial synchronization. To confirm this empirically, we show that a mixture of EEG components is indeed associated with more sinusoidal oscillations compared to the waveform of oscillations in each constituent component. Using simulations, we also show that the spatial mixing of the non-sinusoidal neuronal signals strongly affects the amplitude ratio of the spectral harmonics constituting the waveform. Finally, our simulations show how spatial mixing can affect the strength and even the direction of the amplitude coupling between constituent neuronal harmonics at different frequencies. Validating these simulations, we also demonstrate these effects in real EEG recordings. Our findings have far reaching implications for the neurophysiological interpretation of spectral profiles, cross-frequency interactions, as well as for the unequivocal determination of oscillatory phase. [ABSTRACT FROM AUTHOR]

Inferior olivary activity causes both short-term and long-term changes in cerebellar output underlying motor performance and motor learning. Many of its neurons engage in coherent subthreshold oscillations and are extensively coupled via gap junctions. Studies in reduced preparations suggest that these properties promote rhythmic, synchronized output. However, the interaction of these properties with torrential synaptic inputs in awake behaving animals is not well understood. Here we combine electrophysiological recordings in awake mice with a realistic tissue-scale computational model of the inferior olive to study the relative impact of intrinsic and extrinsic mechanisms governing its activity. Our data and model suggest that if subthreshold oscillations are present in the awake state, the period of these oscillations will be transient and variable. Accordingly, by using different temporal patterns of sensory stimulation, we found that complex spike rhythmicity was readily evoked but limited to short intervals of no more than a few hundred milliseconds and that the periodicity of this rhythmic activity was not fixed but dynamically related to the synaptic input to the inferior olive as well as to motor output. In contrast, in the long-term, the average olivary spiking activity was not affected by the strength and duration of the sensory stimulation, while the level of gap junctional coupling determined the stiffness of the rhythmic activity in the olivary network during its dynamic response to sensory modulation. Thus, interactions between intrinsic properties and extrinsic inputs can explain the variations of spiking activity of olivary neurons, providing a temporal framework for the creation of both the short-term and long-term changes in cerebellar output. [ABSTRACT FROM AUTHOR]

The theory of phase oscillators is an essential tool for understanding population dynamics of pacemaking neurons. GABAergic pacemakers in the substantia nigra pars reticulata (SNr), a main basal ganglia (BG) output nucleus, receive inputs from the direct and indirect pathways at distal and proximal regions of their dendritic arbors, respectively. We combine theory, optogenetic stimulation and electrophysiological experiments in acute brain slices to ask how dendritic properties impact the propensity of the various inputs, arriving at different locations along the dendrite, to recruit or entrain SNr pacemakers. By combining cable theory with sinusoidally-modulated optogenetic activation of either proximal somatodendritic regions or the entire somatodendritic arbor of SNr neurons, we construct an analytical model that accurately fits the empirically measured somatic current response to inputs arising from illuminating the soma and various portions of the dendritic field. We show that the extent of the dendritic tree that is illuminated generates measurable and systematic differences in the pacemaker’s phase response curve (PRC), causing a shift in its peak. Finally, we show that the divergent PRCs correctly predict differences in two major features of the collective dynamics of SNr neurons: the fidelity of population responses to sudden step-like changes in inputs; and the phase latency at which SNr neurons are entrained by rhythmic stimulation, which can occur in the BG under both physiological and pathophysiological conditions. Our novel method generates measurable and physiologically meaningful spatial effects, and provides the first empirical demonstration of how the collective responses of SNr pacemakers are determined by the transmission properties of their dendrites. SNr dendrites may serve to delay distal striatal inputs so that they impinge on the spike initiation zone simultaneously with pallidal and subthalamic inputs in order to guarantee a fair competition between the influence of the monosynaptic direct- and polysynaptic indirect pathways. [ABSTRACT FROM AUTHOR]

Hysteresis, the discrepancy in forward and reverse pathways of state transitions, is observed during changing levels of consciousness. Identifying the underlying mechanism of hysteresis phenomena in the brain will enhance the ability to understand, monitor, and control state transitions related to consciousness. We hypothesized that hysteresis in brain networks shares the same underlying mechanism of hysteresis as other biological and non-biological networks. In particular, we hypothesized that the principle of explosive synchronization, which can mediate abrupt state transitions, would be critical to explaining hysteresis in the brain during conscious state transitions. We analyzed high-density electroencephalogram (EEG) that was acquired in healthy human volunteers during conscious state transitions induced by the general anesthetics sevoflurane or ketamine. We developed a novel method to monitor the temporal evolution of EEG networks in a parameter space, which consists of the strength and topography of EEG-based networks. Furthermore, we studied conditions of explosive synchronization in anatomically informed human brain network models. We identified hysteresis in the trajectory of functional brain networks during state transitions. The model study and empirical data analysis explained various hysteresis phenomena during the loss and recovery of consciousness in a principled way: (1) more potent anesthetics induce a larger hysteresis; (2) a larger range of EEG frequencies facilitates transitions into unconsciousness and impedes the return of consciousness; (3) hysteresis of connectivity is larger than that of EEG power; and (4) the structure and strength of functional brain networks reconfigure differently during the loss vs. recovery of consciousness. We conclude that the hysteresis phenomena observed during the loss and recovery of consciousness are generic network features. Furthermore, the state transitions are grounded in the same principle as state transitions in complex non-biological networks, especially during perturbation. These findings suggest the possibility of predicting and modulating hysteresis of conscious state transitions in large-scale brain networks. [ABSTRACT FROM AUTHOR]

Many collective phenomena in Nature emerge from the -partial- synchronisation of the units comprising a system. In the case of the brain, this self-organised process allows groups of neurons to fire in highly intricate partially synchronised patterns and eventually lead to high level cognitive outputs and control over the human body. However, when the synchronisation patterns are altered and hypersynchronisation occurs, undesirable effects can occur. This is particularly striking and well documented in the case of epileptic seizures and tremors in neurodegenerative diseases such as Parkinson’s disease. In this paper, we propose an innovative, minimally invasive, control method that can effectively desynchronise misfiring brain regions and thus mitigate and even eliminate the symptoms of the diseases. The control strategy, grounded in the Hamiltonian control theory, is applied to ensembles of neurons modelled via the Kuramoto or the Stuart-Landau models and allows for heterogeneous coupling among the interacting unities. The theory has been complemented with dedicated numerical simulations performed using the small-world Newman-Watts network and the random Erdős-Rényi network. Finally the method has been compared with the gold-standard Proportional-Differential Feedback control technique. Our method is shown to achieve equivalent levels of desynchronisation using lesser control strength and/or fewer controllers, being thus minimally invasive. [ABSTRACT FROM AUTHOR]

Sleep spindles are brief oscillatory events during non-rapid eye movement (NREM) sleep. Spindle density and synchronization properties are different in MEG versus EEG recordings in humans and also vary with learning performance, suggesting spindle involvement in memory consolidation. Here, using computational models, we identified network mechanisms that may explain differences in spindle properties across cortical structures. First, we report that differences in spindle occurrence between MEG and EEG data may arise from the contrasting properties of the core and matrix thalamocortical systems. The matrix system, projecting superficially, has wider thalamocortical fanout compared to the core system, which projects to middle layers, and requires the recruitment of a larger population of neurons to initiate a spindle. This property was sufficient to explain lower spindle density and higher spatial synchrony of spindles in the superficial cortical layers, as observed in the EEG signal. In contrast, spindles in the core system occurred more frequently but less synchronously, as observed in the MEG recordings. Furthermore, consistent with human recordings, in the model, spindles occurred independently in the core system but the matrix system spindles commonly co-occurred with core spindles. We also found that the intracortical excitatory connections from layer III/IV to layer V promote spindle propagation from the core to the matrix system, leading to widespread spindle activity. Our study predicts that plasticity of intra- and inter-cortical connectivity can potentially be a mechanism for increased spindle density as has been observed during learning. [ABSTRACT FROM AUTHOR]

Several brain diseases are characterized by abnormally strong neuronal synchrony. Coordinated Reset (CR) stimulation was computationally designed to specifically counteract abnormal neuronal synchronization processes by desynchronization. In the presence of spike-timing-dependent plasticity (STDP) this may lead to a decrease of synaptic excitatory weights and ultimately to an anti-kindling, i.e. unlearning of abnormal synaptic connectivity and abnormal neuronal synchrony. The long-lasting desynchronizing impact of CR stimulation has been verified in pre-clinical and clinical proof of concept studies. However, as yet it is unclear how to optimally choose the CR stimulation frequency, i.e. the repetition rate at which the CR stimuli are delivered. This work presents the first computational study on the dependence of the acute and long-term outcome on the CR stimulation frequency in neuronal networks with STDP. For this purpose, CR stimulation was applied with Rapidly Varying Sequences (RVS) as well as with Slowly Varying Sequences (SVS) in a wide range of stimulation frequencies and intensities. Our findings demonstrate that acute desynchronization, achieved during stimulation, does not necessarily lead to long-term desynchronization after cessation of stimulation. By comparing the long-term effects of the two different CR protocols, the RVS CR stimulation turned out to be more robust against variations of the stimulation frequency. However, SVS CR stimulation can obtain stronger anti-kindling effects. We revealed specific parameter ranges that are favorable for long-term desynchronization. For instance, RVS CR stimulation at weak intensities and with stimulation frequencies in the range of the neuronal firing rates turned out to be effective and robust, in particular, if no closed loop adaptation of stimulation parameters is (technically) available. From a clinical standpoint, this may be relevant in the context of both invasive as well as non-invasive CR stimulation. [ABSTRACT FROM AUTHOR]

Synchronization of neural oscillations as a mechanism of brain function is attracting increasing attention. Neural oscillation is a rhythmic neural activity that can be easily observed by noninvasive electroencephalography (EEG). Neural oscillations show the same frequency and cross-frequency synchronization for various cognitive and perceptual functions. However, it is unclear how this neural synchronization is achieved by a dynamical system. If neural oscillations are weakly coupled oscillators, the dynamics of neural synchronization can be described theoretically using a phase oscillator model. We propose an estimation method to identify the phase oscillator model from real data of cross-frequency synchronized activities. The proposed method can estimate the coupling function governing the properties of synchronization. Furthermore, we examine the reliability of the proposed method using time-series data obtained from numerical simulation and an electronic circuit experiment, and show that our method can estimate the coupling function correctly. Finally, we estimate the coupling function between EEG oscillation and the speech sound envelope, and discuss the validity of these results. [ABSTRACT FROM AUTHOR]

The p53 transcription factor is a regulator of key cellular processes including DNA repair, cell cycle arrest, and apoptosis. In this theoretical study, we investigate how the complex circuitry of the p53 network allows for stochastic yet unambiguous cell fate decision-making. The proposed Markov chain model consists of the regulatory core and two subordinated bistable modules responsible for cell cycle arrest and apoptosis. The regulatory core is controlled by two negative feedback loops (regulated by Mdm2 and Wip1) responsible for oscillations, and two antagonistic positive feedback loops (regulated by phosphatases Wip1 and PTEN) responsible for bistability. By means of bifurcation analysis of the deterministic approximation we capture the recurrent solutions (i.e., steady states and limit cycles) that delineate temporal responses of the stochastic system. Direct switching from the limit-cycle oscillations to the “apoptotic” steady state is enabled by the existence of a subcritical Neimark—Sacker bifurcation in which the limit cycle loses its stability by merging with an unstable invariant torus. Our analysis provides an explanation why cancer cell lines known to have vastly diverse expression levels of Wip1 and PTEN exhibit a broad spectrum of responses to DNA damage: from a fast transition to a high level of p53 killer (a p53 phosphoform which promotes commitment to apoptosis) in cells characterized by high PTEN and low Wip1 levels to long-lasting p53 level oscillations in cells having PTEN promoter methylated (as in, e.g., MCF-7 cell line). [ABSTRACT FROM AUTHOR]

The p53 tumor suppressor protein plays a critical role in cellular stress and cancer prevention. A number of post-transcriptional regulators, termed microRNAs, are closely connected with the p53-mediated cellular networks. While the molecular interactions among p53 and microRNAs have emerged, a systems-level understanding of the regulatory mechanism and the role of microRNAs-forming feedback loops with the p53 core remains elusive. Here we have identified from literature that there exist three classes of microRNA-mediated feedback loops revolving around p53, all with the nature of positive feedback coincidentally. To explore the relationship between the cellular performance of p53 with the microRNA feedback pathways, we developed a mathematical model of the core p53-MDM2 module coupled with three microRNA-mediated positive feedback loops involving miR-192, miR-34a, and miR-29a. Simulations and bifurcation analysis in relationship to extrinsic noise reproduce the oscillatory behavior of p53 under DNA damage in single cells, and notably show that specific microRNA abrogation can disrupt the wild-type cellular phenotype when the ubiquitous cell-to-cell variability is taken into account. To assess these in silico results we conducted microRNA-perturbation experiments in MCF7 breast cancer cells. Time-lapse microscopy of cell-population behavior in response to DNA double-strand breaks, together with image classification of single-cell phenotypes across a population, confirmed that the cellular p53 oscillations are compromised after miR-192 perturbations, matching well with the model predictions. Our study via modeling in combination with quantitative experiments provides new evidence on the role of microRNA-mediated positive feedback loops in conferring robustness to the system performance of stress-induced response of p53. [ABSTRACT FROM AUTHOR]

Cell signaling dynamics and transcriptional regulatory activities are variable within specific cell types responding to an identical stimulus. In addition to studying the network interactions, there is much interest in utilizing single cell scale data to elucidate the non-random aspects of the variability involved in cellular decision making. Previous studies have considered the information transfer between the signaling and transcriptional domains based on an instantaneous relationship between the molecular activities. These studies predict a limited binary on/off encoding mechanism which underestimates the complexity of biological information processing, and hence the utility of single cell resolution data. Here we pursue a novel strategy that reformulates the information transfer problem as involving dynamic features of signaling rather than molecular abundances. We pursue a computational approach to test if and how the transcriptional regulatory activity patterns can be informative of the temporal history of signaling. Our analysis reveals (1) the dynamic features of signaling that significantly alter transcriptional regulatory patterns (encoding), and (2) the temporal history of signaling that can be inferred from single cell scale snapshots of transcriptional activity (decoding). Immediate early gene expression patterns were informative of signaling peak retention kinetics, whereas transcription factor activity patterns were informative of activation and deactivation kinetics of signaling. Moreover, the information processing aspects varied across the network, with each component encoding a selective subset of the dynamic signaling features. We developed novel sensitivity and information transfer maps to unravel the dynamic multiplexing of signaling features at each of these network components. Unsupervised clustering of the maps revealed two groups that aligned with network motifs distinguished by transcriptional feedforward vs feedback interactions. Our new computational methodology impacts the single cell scale experiments by identifying downstream snapshot measures required for inferring specific dynamical features of upstream signals involved in the regulation of cellular responses. [ABSTRACT FROM AUTHOR]

Inhibitory interneurons play critical roles in shaping the firing patterns of principal neurons in many brain systems. Despite difference in the anatomy or functions of neuronal circuits containing inhibition, two basic motifs repeatedly emerge: feed-forward and feedback. In the locust, it was proposed that a subset of lateral horn interneurons (LHNs), provide feed-forward inhibition onto Kenyon cells (KCs) to maintain their sparse firing—a property critical for olfactory learning and memory. But recently it was established that a single inhibitory cell, the giant GABAergic neuron (GGN), is the main and perhaps sole source of inhibition in the mushroom body, and that inhibition from this cell is mediated by a feedback (FB) loop including KCs and the GGN. To clarify basic differences in the effects of feedback vs. feed-forward inhibition in circuit dynamics we here use a model of the locust olfactory system. We found both inhibitory motifs were able to maintain sparse KCs responses and provide optimal odor discrimination. However, we further found that only FB inhibition could create a phase response consistent with data recorded in vivo. These findings describe general rules for feed-forward versus feedback inhibition and suggest GGN is potentially capable of providing the primary source of inhibition to the KCs. A better understanding of how inhibitory motifs impact post-synaptic neuronal activity could be used to reveal unknown inhibitory structures within biological networks. [ABSTRACT FROM AUTHOR]

The circadian clock is a set of regulatory steps that oscillate with a period of approximately 24 hours influencing many biological processes. These oscillations are robust to external stresses, and in the case of genotoxic stress (i.e. DNA damage), the circadian clock responds through phase shifting with primarily phase advancements. The effect of DNA damage on the circadian clock and the mechanism through which this effect operates remains to be thoroughly investigated. Here we build an in silico model to examine damage-induced circadian phase shifts by investigating a possible mechanism linking circadian rhythms to metabolism. The proposed model involves two DNA damage response proteins, SIRT1 and PARP1, that are each consumers of nicotinamide adenine dinucleotide (NAD), a metabolite involved in oxidation-reduction reactions and in ATP synthesis. This model builds on two key findings: 1) that SIRT1 (a protein deacetylase) is involved in both the positive (i.e. transcriptional activation) and negative (i.e. transcriptional repression) arms of the circadian regulation and 2) that PARP1 is a major consumer of NAD during the DNA damage response. In our simulations, we observe that increased PARP1 activity may be able to trigger SIRT1-induced circadian phase advancements by decreasing SIRT1 activity through competition for NAD supplies. We show how this competitive inhibition may operate through protein acetylation in conjunction with phosphorylation, consistent with reported observations. These findings suggest a possible mechanism through which multiple perturbations, each dominant during different points of the circadian cycle, may result in the phase advancement of the circadian clock seen during DNA damage. [ABSTRACT FROM AUTHOR]

Epilepsy—the condition of recurrent, unprovoked seizures—manifests in brain voltage activity with characteristic spatiotemporal patterns. These patterns include stereotyped semi-rhythmic activity produced by aggregate neuronal populations, and organized spatiotemporal phenomena, including waves. To assess these spatiotemporal patterns, we develop a mathematical model consistent with the observed neuronal population activity and determine analytically the parameter configurations that support traveling wave solutions. We then utilize high-density local field potential data recorded in vivo from human cortex preceding seizure termination from three patients to constrain the model parameters, and propose basic mechanisms that contribute to the observed traveling waves. We conclude that a relatively simple and abstract mathematical model consisting of localized interactions between excitatory cells with slow adaptation captures the quantitative features of wave propagation observed in the human local field potential preceding seizure termination. [ABSTRACT FROM AUTHOR]

Fine-scale temporal organization of cortical activity in the gamma range (∼25–80Hz) may play a significant role in information processing, for example by neural grouping (‘binding’) and phase coding. Recent experimental studies have shown that the precise frequency of gamma oscillations varies with input drive (e.g. visual contrast) and that it can differ among nearby cortical locations. This has challenged theories assuming widespread gamma synchronization at a fixed common frequency. In the present study, we investigated which principles govern gamma synchronization in the presence of input-dependent frequency modulations and whether they are detrimental for meaningful input-dependent gamma-mediated temporal organization. To this aim, we constructed a biophysically realistic excitatory-inhibitory network able to express different oscillation frequencies at nearby spatial locations. Similarly to cortical networks, the model was topographically organized with spatially local connectivity and spatially-varying input drive. We analyzed gamma synchronization with respect to phase-locking, phase-relations and frequency differences, and quantified the stimulus-related information represented by gamma phase and frequency. By stepwise simplification of our models, we found that the gamma-mediated temporal organization could be reduced to basic synchronization principles of weakly coupled oscillators, where input drive determines the intrinsic (natural) frequency of oscillators. The gamma phase-locking, the precise phase relation and the emergent (measurable) frequencies were determined by two principal factors: the detuning (intrinsic frequency difference, i.e. local input difference) and the coupling strength. In addition to frequency coding, gamma phase contained complementary stimulus information. Crucially, the phase code reflected input differences, but not the absolute input level. This property of relative input-to-phase conversion, contrasting with latency codes or slower oscillation phase codes, may resolve conflicting experimental observations on gamma phase coding. Our modeling results offer clear testable experimental predictions. We conclude that input-dependency of gamma frequencies could be essential rather than detrimental for meaningful gamma-mediated temporal organization of cortical activity. [ABSTRACT FROM AUTHOR]

In this work we investigate, by means of a computational stochastic model, how tumor cells with wild-type p53 gene respond to the drug Nutlin, an agent that interferes with the Mdm2-mediated p53 regulation. In particular, we show how the stochastic gene-switching controlled by p53 can explain experimental dose-response curves, i.e., the observed inter-cell variability of the cell viability under Nutlin action. The proposed model describes in some detail the regulation network of p53, including the negative feedback loop mediated by Mdm2 and the positive loop mediated by PTEN, as well as the reversible inhibition of Mdm2 caused by Nutlin binding. The fate of the individual cell is assumed to be decided by the rising of nuclear-phosphorylated p53 over a certain threshold. We also performed in silico experiments to evaluate the dose-response curve after a single drug dose delivered in mice, or after its fractionated administration. Our results suggest that dose-splitting may be ineffective at low doses and effective at high doses. This complex behavior can be due to the interplay among the existence of a threshold on the p53 level for its cell activity, the nonlinearity of the relationship between the bolus dose and the peak of active p53, and the relatively fast elimination of the drug. [ABSTRACT FROM AUTHOR]

Cytotoxic T lymphocytes (CTL) are a major factor in the control of HIV replication. CTL arise in acute infection, causing escape mutations to spread rapidly through the population of infected cells. As a result, the virus develops partial resistance to the immune response. The factors controlling the order of mutating epitope sites are currently unknown and would provide a valuable tool for predicting conserved epitopes. In this work, we adapt a well-established mathematical model of HIV evolution under dynamical selection pressure from multiple CTL clones to include partial impairment of CTL recognition, , as well as cost to viral replication, . The process of escape is described in terms of the cost-benefit tradeoff of escape mutations and predicts a trajectory in the cost-benefit plane connecting sequentially escaped sites, which moves from high recognition loss/low fitness cost to low recognition loss/high fitness cost and has a larger slope for early escapes than for late escapes. The slope of the trajectory offers an interpretation of positive correlation between fitness costs and HLA binding impairment to HLA-A molecules and a protective subset of HLA-B molecules that was observed for clinically relevant escape mutations in the Pol gene. We estimate the value of from published experimental studies to be in the range (0.01–0.86) and show that the assumption of complete recognition loss () leads to an overestimate of mutation cost. Our analysis offers a consistent interpretation of the commonly observed pattern of escape, in which several escape mutations are observed transiently in an epitope. This non-nested pattern is a combined effect of temporal changes in selection pressure and partial recognition loss. We conclude that partial recognition loss is as important as fitness loss for predicting the order of escapes and, ultimately, for predicting conserved epitopes that can be targeted by vaccines. [ABSTRACT FROM AUTHOR]

Sleep spindles and K-complexes (KCs) define stage 2 NREM sleep (N2) in humans. We recently showed that KCs are isolated downstates characterized by widespread cortical silence. We demonstrate here that KCs can be quasi-synchronous across scalp EEG and across much of the cortex using electrocorticography (ECOG) and localized transcortical recordings (bipolar SEEG). We examine the mechanism of synchronous KC production by creating the first conductance based thalamocortical network model of N2 sleep to generate both spontaneous spindles and KCs. Spontaneous KCs are only observed when the model includes diffuse projections from restricted prefrontal areas to the thalamic reticular nucleus (RE), consistent with recent anatomical findings in rhesus monkeys. Modeled KCs begin with a spontaneous focal depolarization of the prefrontal neurons, followed by depolarization of the RE. Surprisingly, the RE depolarization leads to decreased firing due to disrupted spindling, which in turn is due to depolarization-induced inactivation of the low-threshold Ca2+ current (IT). Further, although the RE inhibits thalamocortical (TC) neurons, decreased RE firing causes decreased TC cell firing, again because of disrupted spindling. The resulting abrupt removal of excitatory input to cortical pyramidal neurons then leads to the downstate. Empirically, KCs may also be evoked by sensory stimuli while maintaining sleep. We reproduce this phenomenon in the model by depolarization of either the RE or the widely-projecting prefrontal neurons. Again, disruption of thalamic spindling plays a key role. Higher levels of RE stimulation also cause downstates, but by directly inhibiting the TC neurons. SEEG recordings from the thalamus and cortex in a single patient demonstrated the model prediction that thalamic spindling significantly decreases before KC onset. In conclusion, we show empirically that KCs can be widespread quasi-synchronous cortical downstates, and demonstrate with the first model of stage 2 NREM sleep a possible mechanism whereby this widespread synchrony may arise. [ABSTRACT FROM AUTHOR]

Synchronization between neuronal populations plays an important role in information transmission between brain areas. In particular, collective oscillations emerging from the synchronized activity of thousands of neurons can increase the functional connectivity between neural assemblies by coherently coordinating their phases. This synchrony of neuronal activity can take place within a cortical patch or between different cortical regions. While short-range interactions between neurons involve just a few milliseconds, communication through long-range projections between different regions could take up to tens of milliseconds. How these heterogeneous transmission delays affect communication between neuronal populations is not well known. To address this question, we have studied the dynamics of two bidirectionally delayed-coupled neuronal populations using conductance-based spiking models, examining how different synaptic delays give rise to in-phase/anti-phase transitions at particular frequencies within the gamma range, and how this behavior is related to the phase coherence between the two populations at different frequencies. We have used spectral analysis and information theory to quantify the information exchanged between the two networks. For different transmission delays between the two coupled populations, we analyze how the local field potential and multi-unit activity calculated from one population convey information in response to a set of external inputs applied to the other population. The results confirm that zero-lag synchronization maximizes information transmission, although out-of-phase synchronization allows for efficient communication provided the coupling delay, the phase lag between the populations, and the frequency of the oscillations are properly matched. [ABSTRACT FROM AUTHOR]

Kinesin motor proteins drive intracellular transport by coupling ATP hydrolysis to conformational changes that mediate directed movement along microtubules. Characterizing these distinct conformations and their interconversion mechanism is essential to determining an atomic-level model of kinesin action. Here we report a comprehensive principal component analysis of 114 experimental structures along with the results of conventional and accelerated molecular dynamics simulations that together map the structural dynamics of the kinesin motor domain. All experimental structures were found to reside in one of three distinct conformational clusters (ATP-like, ADP-like and Eg5 inhibitor-bound). These groups differ in the orientation of key functional elements, most notably the microtubule binding α4–α5, loop8 subdomain and α2b-β4-β6-β7 motor domain tip. Group membership was found not to correlate with the nature of the bound nucleotide in a given structure. However, groupings were coincident with distinct neck-linker orientations. Accelerated molecular dynamics simulations of ATP, ADP and nucleotide free Eg5 indicate that all three nucleotide states could sample the major crystallographically observed conformations. Differences in the dynamic coupling of distal sites were also evident. In multiple ATP bound simulations, the neck-linker, loop8 and the α4–α5 subdomain display correlated motions that are absent in ADP bound simulations. Further dissection of these couplings provides evidence for a network of dynamic communication between the active site, microtubule-binding interface and neck-linker via loop7 and loop13. Additional simulations indicate that the mutations G325A and G326A in loop13 reduce the flexibility of these regions and disrupt their couplings. Our combined results indicate that the reported ATP and ADP-like conformations of kinesin are intrinsically accessible regardless of nucleotide state and support a model where neck-linker docking leads to a tighter coupling of the microtubule and nucleotide binding regions. Furthermore, simulations highlight sites critical for large-scale conformational changes and the allosteric coupling between distal functional sites. [ABSTRACT FROM AUTHOR]

Traveling waves of neuronal oscillations have been observed in many cortical regions, including the motor and sensory cortex. Such waves are often modulated in a task-dependent fashion although their precise functional role remains a matter of debate. Here we conjecture that the cortex can utilize the direction and wavelength of traveling waves to encode information. We present a novel neural mechanism by which such information may be decoded by the spatial arrangement of receptors within the dendritic receptor field. In particular, we show how the density distributions of excitatory and inhibitory receptors can combine to act as a spatial filter of wave patterns. The proposed dendritic mechanism ensures that the neuron selectively responds to specific wave patterns, thus constituting a neural basis of pattern decoding. We validate this proposal in the descending motor system, where we model the large receptor fields of the pyramidal tract neurons — the principle outputs of the motor cortex — decoding motor commands encoded in the direction of traveling wave patterns in motor cortex. We use an existing model of field oscillations in motor cortex to investigate how the topology of the pyramidal cell receptor field acts to tune the cells responses to specific oscillatory wave patterns, even when those patterns are highly degraded. The model replicates key findings of the descending motor system during simple motor tasks, including variable interspike intervals and weak corticospinal coherence. By additionally showing how the nature of the wave patterns can be controlled by modulating the topology of local intra-cortical connections, we hence propose a novel integrated neuronal model of encoding and decoding motor commands. [ABSTRACT FROM AUTHOR]

The learning mechanism in the hippocampus has almost universally been assumed to be Hebbian in nature, where individual neurons in an engram join together with synaptic weight increases to support facilitated recall of memories later. However, it is also widely known that Hebbian learning mechanisms impose significant capacity constraints, and are generally less computationally powerful than learning mechanisms that take advantage of error signals. We show that the differential phase relationships of hippocampal subfields within the overall theta rhythm enable a powerful form of error-driven learning, which results in significantly greater capacity, as shown in computer simulations. In one phase of the theta cycle, the bidirectional connectivity between CA1 and entorhinal cortex can be trained in an error-driven fashion to learn to effectively encode the cortical inputs in a compact and sparse form over CA1. In a subsequent portion of the theta cycle, the system attempts to recall an existing memory, via the pathway from entorhinal cortex to CA3 and CA1. Finally the full theta cycle completes when a strong target encoding representation of the current input is imposed onto the CA1 via direct projections from entorhinal cortex. The difference between this target encoding and the attempted recall of the same representation on CA1 constitutes an error signal that can drive the learning of CA3 to CA1 synapses. This CA3 to CA1 pathway is critical for enabling full reinstatement of recalled hippocampal memories out in cortex. Taken together, these new learning dynamics enable a much more robust, high-capacity model of hippocampal learning than was available previously under the classical Hebbian model. [ABSTRACT FROM AUTHOR]

Stimulus-induced perturbations from the steady state are a hallmark of signal transduction. In some signaling modules, the steady state is characterized by rapid synthesis and degradation of signaling proteins. Conspicuous among these are the p53 tumor suppressor, its negative regulator Mdm2, and the negative feedback regulator of NFκB, IκBα. We investigated the physiological importance of this turnover, or flux, using a computational method that allows flux to be systematically altered independently of the steady state protein abundances. Applying our method to a prototypical signaling module, we show that flux can precisely control the dynamic response to perturbation. Next, we applied our method to experimentally validated models of p53 and NFκB signaling. We find that high p53 flux is required for oscillations in response to a saturating dose of ionizing radiation (IR). In contrast, high flux of Mdm2 is not required for oscillations but preserves p53 sensitivity to sub-saturating doses of IR. In the NFκB system, degradation of NFκB-bound IκB by the IkB kinase (IKK) is required for activation in response to TNF, while high IKK-independent degradation prevents spurious activation in response to metabolic stress or low doses of TNF. Our work identifies flux pairs with opposing functional effects as a signaling motif that controls the stimulus-sensitivity of the p53 and NFκB stress-response pathways, and may constitute a general design principle in signaling pathways. [ABSTRACT FROM AUTHOR]

We investigate the dynamics of a deterministic finite-sized network of synaptically coupled spiking neurons and present a formalism for computing the network statistics in a perturbative expansion. The small parameter for the expansion is the inverse number of neurons in the network. The network dynamics are fully characterized by a neuron population density that obeys a conservation law analogous to the Klimontovich equation in the kinetic theory of plasmas. The Klimontovich equation does not possess well-behaved solutions but can be recast in terms of a coupled system of well-behaved moment equations, known as a moment hierarchy. The moment hierarchy is impossible to solve but in the mean field limit of an infinite number of neurons, it reduces to a single well-behaved conservation law for the mean neuron density. For a large but finite system, the moment hierarchy can be truncated perturbatively with the inverse system size as a small parameter but the resulting set of reduced moment equations that are still very difficult to solve. However, the entire moment hierarchy can also be re-expressed in terms of a functional probability distribution of the neuron density. The moments can then be computed perturbatively using methods from statistical field theory. Here we derive the complete mean field theory and the lowest order second moment corrections for physiologically relevant quantities. Although we focus on finitesize corrections, our method can be used to compute perturbative expansions in any parameter. [ABSTRACT FROM AUTHOR]